41CHAPTER
3Multiple Linear regression
A
fter reading this chapter you will understand:■ (^) What a multiple linear regression model is.
■ (^) The assumptions about the error terms in a multiple linear regression
model.
■ (^) How the regression coefficients of the model are estimated.
■ (^) The three steps necessary in designing a regression model: specification,
fitting/estimating, and diagnosis.
■ (^) The tests used for determining the significance of the model and each
independent variable.
It is often the case in finance that it is necessary to analyze more than
one variable simultaneously. In Chapter 2, we explained how to estimate a
linear dependence between two variables using the linear regression method.
When there is only one independent variable, the regression model is said to
be a simple linear regression or a univariate regression.
Univariate modeling in many cases is not sufficient to deal with real
problems in finance. The behavior of a certain variable of interest sometimes
needs to be explained by two or more variables. For example, suppose that
we want to determine the financial or macroeconomic variables that affect
the monthly return on the Standard & Poor’s 500 (S&P 500) index. Let’s
suppose that economic and financial theory suggest that there are 10 such
explanatory variables. Thus we have a setting of 11 dimensions—the return
on the S&P 500 and the 10 explanatory variables.
In this chapter and in the next, we explain the multiple linear regres-
sion model to explain the linear relationship between several independent
variables and some dependent variable we observe. As in the univariate
case (i.e., simple linear regression) discussed in Chapter 2, the relationship
between the variables of interest may not be linear. However, that can be
handled by a suitable transformation of the variables.